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Here's the basic response structure:
1NT---
2C = Puppet Stayman. Asks if opener have a five card major.
2D = Transfer. 4+H. GF if 4H.
2H = Transfer. 5+S and INV+.
2S = Range-ask. Bal INV, GF with 6+ clubs, or INV with 6+D.
2NT = INV with 5H and 4S.
3C = Natural INV.
3D = GF 5-5 minors.
3M = (13)(54) or (03)(55) GF.
3NT = To play
4C = COG with 5-5 majors.
4DH = Texas
First lets start with the 2C response, which asks if opener has a five card major. This response can include the following hand types:
a) Weak hand with 5+D
b) Weak hand with 5+S
c) COG hands searching for a 5-3 or 4-4 major fit, may have 3, 4 or 5 card major himself.
d) INV with 4M
e) INV+ with 4-4M
f) GF with 5-4 or 5-5M (SI if 5-5M)
g) Unbal GF with 4S
h) SI with 6+D
That's a lot of hand types, but the primary use case is GF hands searching for a major fit or weak hands with diamonds/spades. Opener bids 2D without a five card major, or 2M with one. Let's take the case where opener have a five card major first.
1NT-2C; 2H---
2S = To play.
2NT = INV.
3C = Puppet to 3D, weak or GF. Could be 6+D or 4S and 5D in this case (if GF).
3D = GF with heart support
3H = INV
3S = GF with 4S and 5+C.
3NT = To play.
4H = To play.
1NT-2C; 2S---
2NT = INV
3C = Puppet to 3D, weak or SI. In this case always 6+D if GF.
3D = ?
3H = GF with spade support.
3S = INV
3NT = To play
It is a bit awkward with these responses when having the unbalanced GF hands, but should probably be ok? Now to the 2D rebid:
1NT-2C; 2D---
2H = Weak with 5S or INV with 4S or unbal GF with 4S.
...2S = Ok?
......2NT = INV with 4S.
......3C = GF with 5+C and 4S.
......3D = GF three-suiter with short hearts.
......3H = GF with 5+D and 4S, short clubs.
......3S = GF with 5+D and 4S, short hearts..
......3NT = SI with 5+D and 4S, doesn't want to show shortness.
2S = INV with 4-4 majors, or GF with 5-4 or 5-5 majors.
...2NT = Min, no major. Same responses as 3C below.
...3C = Max
......3DH = GF transfer with 5-4 majors. Transfer to hearts could be 5-5 majors.
......3S = SI with 4-4 majors.
......3NT = COG with 4-4 majors.
...3M = Min, four card major
2NT = INV with 4H.
3C = SI with 6+D.
3D = COG with 5M (where opener can choose to play 3NT or 4M even though a fit exists). 3H asks major.
3HS = COG with 4oM.
3NT = To play.
4CD = SAT with 6-4 majors.
Now the transfer to hearts, which is either a standard transfer (0+ hcp with 5+H) or unbal GF with 4H. Opener can super-accept etc.
1NT-2D; 2H---
2S = Unbal GF with 4H. Opener usually bids 2NT and then same principle as 1NT-2C; 2D-2H; 2S-3C+.
2NT = INV with 5H.
3C = Unbal GF with 5H, not 4+S, not 5+m.
3D = INV or SI with 6+H
3H = GF with 5-5 hearts + clubs
3S = GF with 5-5 hearts + diamonds
3NT = Wants to play 4H if partner have support.
Since weak hands with spades start with 2C, the transfer to spades promise at least invitational values. The transfer to spades can be made with 5S and 4H and invitational values.
1NT-2H;
2S = Does not accept the invite.
...2NT = INV with 5S and 4H.
...3C+ = GF / INV.
2NT = Max with 2S.
...3C = Unbal GF with 5S, not 4+H, not 5+m.
...3D = INV with 5S and 4H, or SI with 6+S.
...3H = GF with 5-5 spades + clubs.
...3S = GF with 5-5 spades + diamonds.
3C = Max with 3+S. Some scheme here to show shortness and/or side-suit.
The rest of the structure isn't anything special. After 1NT-2S range-ask responder can sign-off in 3C, bid 3D as natural and invitational, sign-off in NT, or bid something else with GF 6+C.